<p>Realistic motion simulation for articulated figures has relied on the solution of linear systems of equations. Sometimes the solution of these equations presents a great deal of numerical difficulty, resulting in unrealistic or spurious motion for the figure or in excessive computation because of small integration intervals. The cause of the difficulty is shown to be related to the physical structure of the figure, not the mathematical formulation. It is shown how to determine the severity of ill conditioning and how to obtain physically meaningful solutions without excessive computations, even when dealing with extremely ill-conditioned configurations.</p>